access icon openaccess pth-order inverse of the Volterra series for multiple-input multiple-output non-linear dynamic systems

A method to determine the pth-order inverse of the Volterra series of multiple-input multiple-output non-linear dynamic systems is presented; it combines time- and frequency-domain techniques to determine the Volterra series of the inverse as a function of the forward system's Volterra series. The method can be used for continuous and discrete time systems. Each operator of non-linear order n of the inverse is a function of the forward system's operators of non-linear order n and lower. It is shown that the p th-order post-inverse is equal to the pth-order preinverse. For the special case that there are no linear cross terms and that the linear memory effects are negligible the kernels of the forward and inverse models are approximately the same. In an example, an approximate inverse model of a model of a concurrent dual band radio frequency amplifier is derived.

Inspec keywords: continuous time systems; nonlinear dynamical systems; nonlinear control systems; Volterra series; MIMO systems; discrete time systems

Other keywords: Volterra series; concurrent dual band radio frequency amplifier; pth-order preinverse; frequency-domain techniques; approximate inverse model; pth-order post-inverse; discrete time systems; time-domain techniques; multiple-input multiple-output nonlinear dynamic systems; continuous time systems; forward system operators

Subjects: Discrete control systems; Multivariable control systems; Nonlinear control systems

References

    1. 1)
      • 26. Bassam, S.A., Helaoui, M., Ghannouchi, F.M.: ‘2D digital predistortion (2D-DPD) architecture for concurrent dual-band transmitters’, IEEE Trans. Microw. Theory Technol., 2011, 59, (10), pp. 25472553.
    2. 2)
      • 13. Eun, C., Powers, E.J.: ‘A new Volterra predistorter based on the indirect learning architecture’, IEEE Trans. Signal Process., 1997, 45, (1), pp. 223227.
    3. 3)
      • 14. Li, L.M., Billings, S.A.: ‘Generalized frequency response functions and output response synthesis for MIMO non-linear systems’, Int. J. Control, 2006, 79, (1), pp. 5362.
    4. 4)
      • 1. Schetzen, M.: ‘The Volterra and Wiener theories of nonlinear systems’ (Krieger Publishing Company, Malabar, FL, 2006).
    5. 5)
      • 24. Amin, S., Händel, P., Rönnow, D.: ‘Digital predistortion of single and concurrent dual band radio frequency GaN amplifiers with strong nonlinear memory effects’, IEEE Trans. Microw. Theory Technol., 2017, 65, (7), pp. 24532464.
    6. 6)
      • 25. Amin, S., Van Moer, W., Händel, P., et al: ‘Characterization of concurrent dual-band power amplifiers using a dual two-tone excitation signal’, IEEE Trans. Instrum. Meas., 2015, 64, (10), pp. 27812791.
    7. 7)
      • 4. Ali, M.T., Wu, R., Mao, L., et al: ‘High frequency CMOS amplifier with improved linearity’, IET Circuits Dev. Syst.., 2014, 8, (6), pp. 450458.
    8. 8)
      • 21. Suryasarman, P.M., Springer, A.: ‘A comparative analysis of adaptive digital predistortion algorithms for multiple antenna transmitters’, IEEE Circuits Syst. Regul. Pap., 2015, 62, (5), pp. 14121420.
    9. 9)
      • 16. Fang, Y., Jiao, L., Pan, J.: ‘MIMO Volterra filter equalization using pth-order inverse approach’. Int. Conf. Acoustics Speech and Signal Processing Proc., Istanbul, Turkey, June 2000, pp. 177180.
    10. 10)
      • 22. Tsimbinos, J., Lever, K.V.: ‘Computational complexity of Volterra based nonlinear compensators’, Electron. Lett., 1996, 32, (9), pp. 852854.
    11. 11)
      • 3. Cheng, C.M., Peng, Z.K., Zhang, W.M., et al: ‘Volterra-series-based nonlinear system modeling and its engineering applications: a state-of-the-art review’, Mech. Syst. Signal Process., 2017, 87, pp. 340364.
    12. 12)
      • 15. Swain, A.K., Billings, S.A.: ‘Generalized frequency response function matrix for MIMO non-linear systems’, Int. J. Control, 2001, 74, (8), pp. 829844.
    13. 13)
      • 6. Schetzen, M.: ‘Theory of pth-order inverses of nonlinear systems’, IEEE Trans. Circuits Syst., 1976, CAS-23, (5), pp. 285291.
    14. 14)
      • 5. Sandler, R.A., Deadwyler, S.A., Hampson, R.E., et al: ‘System identification of point-process neural systems using probability based Volterra kernels’, J. Neurosci. Methods, 2015, 240, pp. 179192.
    15. 15)
      • 27. Alizadeh, M., Amin, S., Rönnow, D.: ‘Measurement and analysis of frequency-domain Volterra kernels of nonlinear dynamic 3 × 3 MIMO, IEEE Trans. Instrum. Meas., 2017, 66, (7), pp. 18931905.
    16. 16)
      • 17. Ghannouchi, F., Younes, M., Rawat, R.: ‘Distortion and impairments mitigation and compensation of single- and multi-band wireless transmitters (invited)’, IET Microw. Antennas Propag., 2013, 7, (7), pp. 518534.
    17. 17)
      • 8. Beidas, B.F.: ‘Adaptive digital signal predistortion for nonlinear communication systems using successive methods’, IEEE Trans. Commun., 2016, 64, (5), pp. 21662175.
    18. 18)
      • 11. Tang, C., Zhang, L., Zhang, Y., et al: ‘Nonlinear revised error aided feedback equalization in high-speed satellite communication’, Telecommun. Syst., 2017, 66, (2), pp. 243251, doi: 10.1007/s11235-017-0282-7.
    19. 19)
      • 20. Amin, S., Landin, P., Händel, P., et al: ‘Behavioral modelling and linearization of crosstalk and memory effects in radio frequency MIMO transmitters’, IEEE Trans. Microw. Theory Tech., 2014, 62, (4), pp. 810823.
    20. 20)
      • 12. Lashkari, K.: ‘A novel Volterra-Wiener model for equalization of loudspeaker distortions’. Proc. Int. Conf. Acoustics Speech and Signal Processing Proc., Toulouse, France, May 2006, vol. 5, pp. 117120.
    21. 21)
      • 10. Björsell, N., Isaksson, M., Händel, P., et al: ‘Kautz–volterra modelling of analogue-to-digital converters’, Comput. Standards Interf., 2010, 32, pp. 126129.
    22. 22)
      • 2. Borys, A.: ‘Nonlinear aspects of telecommunication: discrete Volterra series and nonlinear echo cancellation’ (CRC Press LLC, Florida, 2001).
    23. 23)
      • 18. Beidas, B.F.: ‘Intermodulation distortion in multicarrier satellite systems: analysis and turbo volterra equalization’, IEEE Trans. Commun., 2011, 59, (6), pp. 15801590.
    24. 24)
      • 9. Berenguer, P.W., Nölle, M., Molle, L., et al: ‘Nonlinear digital pre-distortion of transmitter components’, J. Lightw. Technol., 2016, 34, (8), pp. 17391745.
    25. 25)
      • 19. Zenteno, E., Piazza, R., Bhavani Shankar, M.R., et al: ‘Multiple-input multiple-output symbol rate signal digital predistorter for non-linear multi-carrier satellite channels’, IET Commun., 2015, 9, (16), pp. 20532059.
    26. 26)
      • 7. Isaksson, M., Rönnow, D.: ‘A parameter-reduced Volterra model for dynamic RF power amplifier modeling based on orthonormal basis functions’, Int. J. RF Microw. Comput. Aided Eng., 2007, 17, (6), pp. 542551.
    27. 27)
      • 23. Glad, T., Ljung, L.: ‘Control theory: multivariable and nonlinear methods’ (Taylor and Francis, London, UK, 2000).
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